Let us see.

a=-7, d=1.5, and Sn=-14.

I assumea=-7is actually a1 = -7

So,

an = a1 +(n-1)d

an = -7 +(n-1)(1.5)

an = 1.5n -8.5 -----------(i)

And,

Sn = (n/2)(a1 +an)

-14 = (n/2)(-7 +1.5n -8.5)

-28 = n(1.5n -15.5)

-28 = 1.5n^2 -15.5n

1.5n^2 -15.5n +28 = 0

Using the Quadratic Formula,

n = {15.5 +,-sqrt[(15.5)^2 -4(1.5)(28)]} / 2(1.5)

n = {15.5 +,-8.5} /3

n = 8 or 2.333

Reject the n=2.333 because n is the number of terms in the sequence/series. So n has to be a positive integer always.

Therefore, n = 8 -----------answer.